8. Testing for Differences in Means and Proportions: Independent Samples t-test
Independent Samples t-test: Test Statistic and p-value
A psychologist wants to examine the effect of mental effort on memory recall. To investigate this matter, two versions of the same text are prepared: one printed in a large and easy-to-read font, and the other in a small and hard-to-read font.
A total of #98# subjects are recruited. Approximately half of the subjects are given the easy-to-read text #(X_1)# and the other half are given the hard-to-read text #(X_2)#. Both groups are given #20# minutes to study the text, after which they are tested on how well they remember what they have read.
The psychologist plans on using an independent samples #t#-test to determine whether there is a significant difference in the memory performance between the two groups, at the #\alpha = 0.05# level of significance.
State the null and alternative hypothesis of the proposed test.
A total of #98# subjects are recruited. Approximately half of the subjects are given the easy-to-read text #(X_1)# and the other half are given the hard-to-read text #(X_2)#. Both groups are given #20# minutes to study the text, after which they are tested on how well they remember what they have read.
The psychologist plans on using an independent samples #t#-test to determine whether there is a significant difference in the memory performance between the two groups, at the #\alpha = 0.05# level of significance.
State the null and alternative hypothesis of the proposed test.
#H_0 : \mu_1 - \mu_2\,\,\,\,#
#H_a : \mu_1 - \mu_2\,\,\,\,#
#H_a : \mu_1 - \mu_2\,\,\,\,#
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